Analytical Solution of the Three-Dimensional Laplace Equation in Terms of Linear Combinations of Hypergeometric Functions

Antonella Lupica, Clemente Cesarano, Flavio Crisanti and Artur Ishkhanyan
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Antonella Lupica: Department of Economics, Engineering, Society and Business Organization (DEIm), University of Tuscia, Largo dell’Università, 01100 Viterbo, Italy
Clemente Cesarano: Section of Mathematics, International Telematic University Uninettuno, 00186 Roma, Italy
Flavio Crisanti: Department of Economics, Engineering, Society and Business Organization (DEIm), University of Tuscia, Largo dell’Università, 01100 Viterbo, Italy
Artur Ishkhanyan: Department of General Physics, Russian-Armenian University, Yerevan 0051, Armenia

Mathematics, 2021, vol. 9, issue 24, 1-16

Abstract: We present some solutions of the three-dimensional Laplace equation in terms of linear combinations of generalized hyperogeometric functions in prolate elliptic geometry, which simulates the current tokamak shapes. Such solutions are valid for particular parameter values. The derived solutions are compared with the solutions obtained in the standard toroidal geometry.

Keywords: Laplace equation; Heun equation; analytic solution; cap-cyclide geometry; standard toroidal geometry; hypergeometric functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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